A model of persistent breaking of continuous symmetry

Abstract

We consider a UV-complete field-theoretic model in general dimensions, including $d=2+1$, that exhibits spontaneous breaking of continuous symmetry, persisting to arbitrarily large temperatures. Our model consists of two copies of the long-range vector models, with $O(m)$ and $O(N-m)$ global symmetry groups, perturbed by double-trace operators. Using conformal perturbation theory we find weakly-coupled IR fixed points for $N\ge 6$ that reveal a spontaneous breaking of global symmetry. Namely, at finite temperature the lower rank group is broken, with the pattern persisting at all temperatures due to scale-invariance. We provide evidence that the models in question are unitary and invariant under full conformal symmetry. Our work generalizes recent results, which considered the particular case of $m=1$ and reported persistent breaking of the discrete ${\mathbb{Z}}_2=O(1)$. Furthermore, we show that this model exhibits a continuous family of weakly interacting field theories at finite $N$.

arXiv commentV2: references and minor changes in the text

References in corpus (46)

• Comments on Abelian Higgs Models and Persistent Order
• A scaling theory for the long-range to short-range crossover and an infrared duality
• Conformal Invariance in the Long-Range Ising Model
• Unitarity violation at the Wilson-Fisher fixed point in 4-epsilon dimensions
• Long-range critical exponents near the short-range crossover
• A Study of Quantum Field Theories in AdS at Finite Coupling
• IS THERE A DOMAIN WALL PROBLEM?
• Is there a monopole problem?
• Circle compactification and 't Hooft anomaly
• On the Hohenberg-Mermin-Wagner theorem and its limitations
• The Random-Bond Ising Model in 2.01 and 3 Dimensions
• The crossover region between long-range and short-range interactions for the critical exponents
• Thermal Order in Conformal Theories
• Bootstrapping the long-range Ising model in three dimensions
• General Properties of Multiscalar RG Flows in $d=4-\epsilon$
• A Complete Renormalization Group Trajectory Between Two Fixed Points
• Exotic Hairy Black Holes
• QCD on a small circle
• Renormalization Group Patterns and C-Theorem in More Than Two Dimensions
• Superfluid black branes in AdS_4\times S^7
• CRITICAL (Phi^{4}_{3,ε})
• $O(N)$ Models with Boundary Interactions and their Long Range Generalizations
• Beyond freeze-in: Dark Matter via inverse phase transition and gravitational wave signal
• Exotic holographic RG flows at finite temperature
• O(N) and O(N) and O(N)
• Critical exponents for long-range O(n) models below the upper critical dimension
• Quantum Distillation of Hilbert Spaces, Semi-classics and Anomaly Matching
• Klebanov-Strassler black hole
• Higher Anomalies, Higher Symmetries, and Cobordisms III: QCD Matter Phases Anew
• Long-range multi-scalar models at three loops
• Thermal order in holographic CFTs and no-hair theorem violation in black branes
• A model of persistent breaking of discrete symmetry
• The free and safe fate of symmetry non-restoration
• The fate of the conformal order
• Thermal order in large N conformal gauge theories
• Symmetry Nonrestoration in a Gross-Neveu Model with Random Chemical Potential
• The bi-conical vector model at $1/N$
• SUGRA/Strings like to be bald
• Symmetry breaking at high temperatures in large N gauge theories
• Compactified holographic conformal order
• High Temperature Symmetry Nonrestoration
• Long-range fermions and critical dualities
• Observing primordial magnetic fields through Dark Matter
• Rochelle salt: a prototype of particle physics
• Critical long-range vector model in the UV
• Long-Range Vector Models at Large N

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• RG studies of scalar-field models of long-range interactions
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